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| We investigate the long term behavior in terms of fi nite dimensional global and exponential attractors, as time goes to in finity of solutions to semilinear reaction-diff usion equations on non-smooth domains subject to nonlocal Robin boundary conditions, characterized by the presence of fractional diffusion on the boundary. Our results are of general character and apply to a large class of irregular domains, including domains with a fractal-like geometry. We recover the most of the existing results on existence, regularity, uniqueness, stability, attractor existence, and finite dimension, which are known for the reaction-diff usion equation in smooth domains. The framework we develop also makes possible a number of new results for all diff usion models in other non-smooth settings. |
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